Terms Definition and 1000 Threads

I'm really not sure as to how I should be interpreting expressing t in terms of c. Any help would be appreciated, thanks

Isometries ... Remarks by Garling including terms "necessary" and "sufficient" ... I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric...

Here is the problem: Let ##C## be a convex disc in the plane, and ##C_1## and ##C_2## be two translates of ##C##. Prove that ##C_1## and ##C_2## are non-crossing, that is, it isn't possible that both ##C_1 - C_2## and ##C_2 - C_1## are non-connected. Here is my question: What exactly do the...

We have the retarded magnetic vector potential ##\mathbf{A}(\mathbf{r},t) = \dfrac{\mu_0}{4\pi} \int \dfrac{\mathbf{J}(\mathbf{r}',t_r)}{|\mathbf{r}-\mathbf{r}'|} \mathrm{d}^3 \mathbf{r}'## And its curl ##\mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}'...

Express function as a trigonometric function of x $$\sin(4x)$$ use $\sin2a=2\sin a\cos a$ then $$\sin4x=2\sin 2x\cos 2x$$ with $\cos(2x) = \cos^2(x)-\sin^2(x)$ replace again $$\sin 4x=4\sin x\cos x+\cos^2(x)-sin^2(x)$$ ok not real sure if this is what they are...

While doing some calculations I came across some terms which are ##\frac{(v•\vec \nabla)v}{a(t)}## and ##\vec \nabla•[\rho(1+\delta)v]## where all quantities have spatial dependence other than "a" which has only time dependence , the first term here is canceled and the the second term is...

For the b following: kQ/R=kq/L L=πR kQ/R=kq/πR πQ=q

Hello. As I understand it, Kepler's 2nd law of planetary motion can be explained through conservation of energy or conservation of angular momentum. I am having trouble with the conservation of energy explanation. We know that the sum of potential and kinetic energy of a planet in orbit around...

Hi, Kindly consider the Question 4.8 on the following link http://parallelcomp.uw.hu/ch04lev2sec18.html ##t_s## = start up time ##t_w## = per-word transfer time m = size of message p = number of processors The total time for communication for ##logp## steps is: ##T = (t_s + t_w*m) * log_2 p##...

Perhaps that statement is just saying how big the t-value is. Like, in this case: t = (1.0 - 0.98) / 0.1 = 0.1 So we can say that our measured value is within 1 sigma from the other measured value. In this case, do we just ignore the uncertainties of the other measured/reference value? It's...

Here's what the picture in the textbook looks like (it kept being too unclear when trying to take a picture so I had to replicate it on Desmos, however my replication is identical to the graph provided in the question. As for the rest of the question... I'm completely stumped. I should note...

f(x)=sinx+cosx getting really frustrated with my math teacher. gives us forumlas for things but then barely shows us how to use them if at all and then throws problems at that we have to make sense of ourself. why can't math teachers teach? anyway, the question is express f(x)=sinx+cosx in...

Could someone, in laymen's terms explain to me what stochastic mechanics is?

I am reading a textbook quantum physics by stephen gasiorowicz. And he defines a wavefunction in this form, $$Ψ(x,t)=\int_{-∞}^{∞}A(k)e^{i:(kx-ωt)}dk$$ I did not understand why its a function of ##k## or why even we are taking integral with respect to ##k## ? Is ##k## actually means momentum...

The Standard Model Lagrangian contains terms like these: ##-\partial_\mu \phi^+ \partial_\mu\phi^-## ##-\frac{1}{2}\partial_\nu Z^0_\mu\partial_\nu Z^0_\mu## ##-igc_w\partial_\nu Z^0(W^+_\mu W^-_\nu-W^+_\nu W^-_\mu)## How should one interpret the "derivative particle fields" like...

Homework Statement For $$f_x(x)=4x^3 ; 0 \leq x \leq 1$$ Find the PDF for $$ Y < y=x^2$$ The Attempt at a Solution So, we take the domain on x to be: $$0\leq x \leq \sqrt y$$ and integrate: $$ \int_0^{\sqrt y} f_x(x) dx = \int_0^{\sqrt y} 4x^3 dx$$ Do we integrate with respect to x or y...

Homework Statement Prove that $$\begin{align*}\mathfrak{T}_L(x) &= \frac{1}{2}\psi_L^\dagger (x)\sigma^\mu i\partial_\mu\psi_L(x) - \frac{1}{2}i\partial_\mu \psi_L^\dagger (x) \sigma^\mu\psi_L(x) \\ \mathfrak{T}_R(x) &= \frac{1}{2}\psi_R^\dagger (x)\bar{\sigma}^\mu i\partial_\mu\psi_R(x) -...

I've just started using Mathematica and I'm still trying to get used to how things are properly done with it. I tried to do a calculation (this one: https://www.physicsforums.com/threads/lagrangian-of-a-driven-pendulum-landau-problem.965714/) and I had to neglect some terms in an expression. Is...

I would like to have someone who would be willing to explain me what is a like term and an unlike term in terms of set theory. I'm just an high-scool student, but I really would like to understand it from that point of view anyway. It doesn't have to be a 1000 pages long of explanations.

I apologize in advance if any formatting is weird; this is my first time posting. If I am breaking any rules with the formatting or if I am not providing enough detail or if I am in the wrong sub-forum, please let me know. 1. Homework Statement Using Euler's formula : ejx = cos(x) + jsin(x)...

I have attached a picture of what I want Matlab to do. I basically want Matlab to show the list of independent variable 'n' and then another column showing the terms when n=0...10. Some of the outputs are in variable form and others in numerical form. My attempt so far is stated below. I have no...

Hi! Here's a tricky thermodynamics problem, I hope you can help with it. 1. Homework Statement The boundary between two different materials can be divided into two different kind of phases: bulk phases and surface phases. For example, let's consider a boundary between water and air. We can...

Homework Statement Solve this, $$\frac{\partial}{\partial x^{\nu}}\frac{3}{(q.x)^3}$$ where q is a constant vector. Homework EquationsThe Attempt at a Solution $$\frac{\partial}{\partial x^{\nu}}\frac{3}{(q.x)^3}=3\frac{\partial(q.x)^{-3}}{\partial (q.x)}*\frac{\partial (q.x)}{\partial x^{\nu}}...

So far i have. 12) area of full circle is πr² area of sector is (120/360)(πr²) or 12π 13) same area is (270/360)(πr²) Am i correct?

So far i have 270/360× (pi)r^ i don't know what to do next please help.

Homework Statement I'm stuck at my particle physics exercise about 4-component chiral fields. The following problem is given: "Derive the expression for the QED Lagrangian in terms of the four component right-handed and left-handed Dirac fields ##\Psi_R(x)## and ##\Psi_L(x)##, respectively."...

What do you think we are going to evolve into or adapt to in the far future or mutations arise that will cause some kind of change in our features and maybe even intelligence, strength, physical attributes. Also do you think it will be the entire human race that will evolve in the same way or do...

Hey guys, I've got this problem I've been trying to solve, but it makes little sense to me. I've tried a few things, but I feel like with each method, I've made no progress, and I haven't been able to make the problem make any more sense to me by trying those things. Here's the question: The...

Homework Statement Prove that if ##(a_n)## is a decreasing sequence of positive numbers and ##\sum a_n## converges, then ##\lim na_n = 0## Homework EquationsThe Attempt at a Solution Let ##\epsilon >0##. By the Cauchy criterion there exists an ##N\in \mathbb{N}## such that ##\forall n\ge m\ge...

Hi, here I am again. This is also related to my previous threads. My question is: How do I calculate the power of generator in terms of speed(rpm) from a drive system (such as belt and chain drives)?

The answer is ja/j-p kms but I have no idea how to get there

Homework Statement Homework EquationsThe Attempt at a Solution 4x^2-2xy=2-3y^2 x(4x-2y)=2-3y^2 then I'm stuck[/B]

Hello! I am a bit confused about the sign of the ##L\frac{dI}{dt}## term in the circuits (DC circuits). In my book it is defined with a minus, on wikipedia it is defined with a plus and I am not sure which one should I use. I can pick any sign I want and the result will come out right...

Homework Statement Problem 16.39 [/B] The viscous force of a liquid in laminar flow through length L is given by ##F_v=4\pi\etaL v_m## where ##\eta## is liquid viscosity and ##v_m## is maximum velocity of the fluid. Find an expression for ##v_m## in terms of p1, p2 (pressure at each end) and...

Ahmad has x marbles. He has 40 more marbles than Weiming a) Find the total number of marbles that Ahmad and Weiming have in terms of x. my answer: x + x + 40. So 2x + 40 b) Ahmad has 55 marbles. How many marbles do they have altogether? my answer: 2(55)+ 40 = 150

Homework Statement The spectrum shows the series 3p - nd, n = 4 - 7 in Na as well as the resonance line 3s - 3p, with the experimental vacuum wavelengths in Å.Calculate the quantum defect for the nd ##^2D## n = 4-7 terms. Estimate, as accurately as possible, the wavelength for 3p - 8d. The...

At a post office, there are three parcels of different masses. The mass of the first parcel is y grams. The mass of the second parcel is 500 grams greater than that of the first parcel. The third parcel is 210 grams lighter than the first parcel. a) Find the total mass, in grams, of the three...

Ann had some stickers. She gave y stickers to each of her 7 friend and had 12 stickers left. a) Find the number of stickers Ann had at first in terms of y. my answer: 7y + 12b) Each friend received 9 stickers. How many stickers did Ann have at first? my answer: 7*9 + 12 = 75

I've been wondering if there is an expression for the magnitude of the proper acceleration of an observer in terms of three-velocities and three-accelerations. I didn't find any, so I took a stab at calculating it. However, it was not at all convenient to do the calculations without 4-vectors...

In a problem from Hartle's Gravity, we are asked to express the line element in non-Cartesian coordinates u, v which are defined with respect to x, y. I have no problem getting the new expression for the line element, but then we are asked if the new coordinate curves intersect at right angles...

What is the radiation and non-radiation terms in the equation B for a moving charged particle. How can I express the result in a tensor form? Thanks!

Homework Statement A point charge q sits at the origin. A magnetic field ##\mathbf{B} (\mathbf{r})=B(x,y)\mathbf{\hat{z}}## fills all of space. The problem asks us to write down an expression for the total electromagnetic field angular momentum ##\bf{L_{EM}}##, in terms of q and the magnetic...

Homework Statement The stability of a spinning body may be explored by using equation (3.40), with no torque components present. It will be assumed here that the spin is about the z -axis and has a rate ωZ = S. Homework Equations $$I_{xx}\dot{ω} - (I_{yy}-I_{zz})Sω_y = 0$$ $$I_{yy}\dot{y} -...

I saw a post where someone was granted access to a 1.5 Tesla MRI. After some research I discovered a 3 Tesla MRI. How strong is this magnet?

Hello, can someone show me how 2.158 radians can also be written as .687pi? I need to learn how to do this so I can write my answer in terms of pi as opposed to 2.158. Thank you in advance. Yeny

For a DEQ like this: y = y( x ) a y'''' + b y''' + c y'' + d y' + f y = g( x ) where a, b, c, d, f are constants. I would think it would be called a "constant coefficient DEQ", but a DEQ like this would also be called this a y y'' + b ( y' )2 = g( x ) but I am only interested in...

Homework Statement S = 1+ x/1! +x2/2! +x3/3! +...+xn/n! To find S in simple terms. Homework Equations None The Attempt at a Solution I tried with Taylor's expansion, coshx and sinhx expansions. But cannot see consequence.

The Helmholtz function differential form for a reversible process is: dF = -SdT - PdV, as for a reversible process δW (by system/here an (ideal) gas) = PdV and dS = δQ/T. Therefore, for a reversible isothermal process, dT = 0 and hence dF = -PdV. Therefore, the work done by the system is W =...

Hi. The induced emf is given by -d/dt ∫B.dS but when the time derivative is taken inside the integral sign this becomes -∫ ∂B /∂t.dS . Why isn't B.dS differentiated using the product rule giving an extra term inside the integral sign ? For some reason the integral sign is appearing as a small...

Homework Statement https://imgur.com/DUdOYjE The problem (#58) and its solution are posted above. Homework Equations I understand that I can approach this two different ways. The first way being the way shown in the solution, and the second way, which my professor suggested, being a Direct...